How do I multiply and divide indices?

First you need to understand what an index (or power) is. It’s just a compact way of writing a number multiplied by itself a number of times. For example:

 34 = 3x3x3x3 and a2  = axa.

If two indices have the same base number (big number at the bottom) then they can be multiplied easily.

For example, if you wanted to find 23 x 24:

First you can write this out in full.

23 x 24 = (2x2x2) x (2x2x2x2)

This is just 2 multiplied by itself 7 times which we can write as 27.

The trick to multiplying indices without writing them out in full each time is just to add the powers together. In the example above the powers are 3 and 4.

3+4 = 7 so 23 x 24 = 27.

Dividing indices is very similar, only instead of adding the powers you subtract them.

E.g. Find 26 / 22:

These have the same base number (2) so we’re good to go.

Subtract the powers:

6 - 2 = 4

This gives you the power of 2 in the answer:
26 / 22 = 24

That’s all there is to multiplying and dividing indices. When multiplying, add the powers. When dividing, subtract!

Answered by Sarah M. Maths tutor

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